No, you should not get just . The second time around, the two boundary terms from the Leibniz integral rule are not both zero. Check the rule a little more carefully.

A quick check-in, then I'll get out of the way of the main discussion. The Leibniz rule. That is essentially the Fundamental Theorem mixed in with the chain rule, right? (I know that's only a brief description, I can fill in the details on my own if that is where it comes from.)

A quick check-in, then I'll get out of the way of the main discussion. The Leibniz rule. That is essentially the Fundamental Theorem mixed in with the chain rule, right? (I know that's only a brief description, I can fill in the details on my own if that is where it comes from.)